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Full text of "Pitch of Frequency-modulated signals"

PITCH OF FREQUENCY-MODULATED 

SIGNALS 



By 
KEENES DELANEY McCLELLAND 



A DISSERTATION PRESENTED TO THE GRi'UJUATE COUNCIL OF 

THE UNIVERSITY OF FLORIDA 

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOB THE 

DEGREE OF DOCTOR OF PHILOSOPHY 



UNIVERSITY OF FLORIDA 
1968 



To 



Professor C. Albro Newton 



ACKNOWLEDGMENTS 

The writer wishes to express his sincere apprecia- 
tion to Dr. John F. Brandt for his encouragement and guidance 
in the planning and execution of the present research, but 
more especially for the benefit of his skill as a researcher 
and patience as a teacher. 

The author is indebted to the members of the disserta- 
tion committee for their interest and constructive criticism. 
Thanks go to the faculty and students of the Communication 
Sciences Laboratory of the University of Florida for their 
support and assistance. Special thanks also go to Dr. Donald 
C. Teas and Dr. Arnold Paige who read and criticized the 
original manuscript and made many valuable suggestions. 

The work of my wife Nancy in the preparation of graphs, 
charts and the typing of preliminary drafts was invaluable. 

Finally, appreciation is extended to the Vocational 
Rehabilitation Administration for financial support in the 
form of a VRA traineeship. In addition, the research was 
supported from funds provided by the Graduate School of the 
University of Florida and the National Institutes of Health 
(Grant NB 06459) , 



111 



TABLE OF CONTENTS 

Page 

LIST OF TABLES . » . . . V 

LIST OF FIGURES vi 

CHAPTER 

I INTRODUCTION 1 

II PROCEDURE 6 

Apparatus q 

Stimuli 9 

Subjects 9 

General Procedure 10 

III RESULTS 11 

Effects of Modulation Frequency 

(20dB SL) 18 

Effects of Modulation Frequency 

( 50dB SL) 20 

Subject Variability 21 

IV DISCUSSION 24 

V SUMMARY 3 7 

APPENDIX A ELECTRICAL SPECTRA AND EARPHONE 

FREQUENCY RESPONSE CURVES 41 

APPENDIX B INDIVIDUAL SUBJECT PITCH MATCH DATA . „ 48 

BIBLIOGRAPHY .......... .... 69 

BIOGRAPHICAL SKETCH ................ 72 



iv 



LIST OF TABLES 



Table Page 

1 Experimental conditions. The X's in 

the table represent combinations 
of modulating and carrier frequen- 
cies, ' -9 

2 Frequency modulation stimulus 

parameter s . 26 



V 



LIST OF FIGURES 



Fi gur e 
1 
2 



Schematic drawing of equipment. 

Deviation in semi-tones of grouped pitch 
judgments in 20-cent intervals from 
the carrier frequency for conditions 
300/20 (A) and 300/200 (B). Data 
collected at 20dB SL . The arrows 
represent spectral Information as 
explained in the text. 

Deviation in semi-tones of grouped pitch 
judgments in 20-cent intervals from the 
carrier frequency for conditions 1000/20 
(A) and 1000/200 (B). Data collected at 
20dB SL , 



Page 
8 



12 



13 



Deviation in semi-tones grouped pitch 
judgments in 20-cent intervals from 
the carrier frequency for conditions 
3000/20 (A), 3000/200 (B) and 3000/2000 
(C). Data collected at 20dB SL . 



14 



Deviation in semi-tones of grouped pitch 
judgments in 20-cent intervals from 
the carrier frequency for conditions 
300/20 (A) and 300/200 (B) . Data 
collected at 50dB SL . 



15 



Deviation in semi-tones of grouped pitch 
judgments in 20-cent intervals from 
the carrier frequency for conditions 
1000/20 (A) and 1000/200 (B), Data 
collected at 50dB SL . 



16 



VI 



Deviation in semi-tones of grouped pitch 
judgments in 20-cent intervals from 
the carrier frequency for conditions 
3000/20 (A), 3000/200 (B) and 3000/2000 
(C). Data collected at 50dB SL , 



17 



Representation of between-subject pitch 

matches . 



22 



Sensitivity of the ear as a function of 

frequency (after Stevens and Davis, 1938) 



29 



10 Critical bandwidth based on the minimum 

frequency difference between the harmonics 
of a complex tone necessary for them to 
be heard separately, as a function of 
frequency (after Plorap and Mimpen, 1968). 



31 



11 Electrical spectra for 300/20 (A) and 

300/200 (B). Analyzing bandwidth was 
10 Hz. 



42 



12 Electrical spectra for 1000/20 (A) and 

1000/200 (B) . Analyzing bandwidth was 
10 Hz. 



43 



13 Electrical spectra for 3000/20 (A) and 
3000/200 (B). Analyzing bandwidth 

was 10 Hz . 



44 



14 Electrical spectrum for 3000/2000. An- 
alyzing bandwidth was 10 Hz. 



45 



15 Earphone frequency response curve for 
Earphone A. 



46 



16 Earphone frequency response curve for 
Earphone B. 



47 



17 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject DF 
for conditions 300/20 and 300/200 
at 20 and 50dB SL . 



4@ 



Vll 



18 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject DF 
for conditions 1000/20 and 1000/200 
at 20 and 50dB SL . 



50 



19 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject DF 
for conditions 3000/20 and 3000/200 
at 20 and 50dB SL . 



51 



20 Deviation in semi-tones of pitch judg- 

ments in 20-cent intervals from the 
carrier frequency from subject DF for 
conditions 3000/2000 at 20 and 50dB SL 

21 Deviation in semi-tones of pitch judg- 

ments in 20-cent intervals from the 
carrier frequency from subject NM for 
conditions 300/20 and 300/200 at 20 
and 50dB SL . 



52 



53 



22. Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject NM for 
conditions 1000/20 and 1000/200 at 20 
and 50dB SL . 



54 



23 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject NM for 
conditions 3000/20 and 3000/200 at 20 
and 50dB SL . 



55 



24 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject NM for 
conditions 3000/2000 at 20 and 50dB SL 



56 



25 Deviation in semi-tones of pitch judg- 
ments in 20-cent intervals from the 
carrier frequency from subject TM for 
conditions 300/20 and 300/200 at 20 
and 50dB SL , 



57 



Vlll 



26 Deviation in semi-tones of pitch judg- 
ments in 20-cent intei'vals from the 
carrier frequency from subject TM for 
conditions 1000/20 and 1000/200 at 20 
and 50dB SL. 



58 



27 Deviation in semi-tones of pitch judg- 

ments in 20-cent intervals from the 
carrier frequency from, subject TM for 
conditions 3000/20 and 3000/200 at 20 
and 50dB SL . 

28 Deviation in semi-tones of pitch judg- 

ments in 20-cent intervals from the 
carrier frequency from subject TM for 
conditions 3000/2000 at 20 and 50dB SL 



59 



60 



29 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject CH for conditions 
300/20 and 300/200 at 20 and 50dB SL . 



61 



30 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject CH for conditions 
1000/20 and 1000/200 at 20 and 50dB SL . 



6 2 



31 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject CH for conditions 
3000/20 and 3000/200 at 20 and 50dB SL . 



63 



32 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject CH for conditions 
3000/2000 at 20 and 50dB SL . 



6 4 



33 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject JH for conditions 
300/20 and 300/200 at 20 and 50dB SL . 



6 5 



34 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject JH for conditions 
1000/20 and 1000/200 at 20 and 50dB SL . 



XX 



35 Deviation in semi-tones of pitch judgments 
in 20-cent intei-vals from the carrier 
frequency from subject JH for conditions 
3000/20 and 3000/200 at 20 and 50dB SL . 



67 



36 Deviation in semi-tones of pitch judgments 
in 20-cent intervals from the carrier 
frequency from subject JH for conditions 
3000/2000 at 20 and 50dB SL . 



68 



CHAPTER I 



INTRODUCTION 



The psychophysical phenomenon of pitch has long been 
considered to be related to a process of mechanical frequen- 
cy analysis approximately a Fourier analysis (von Helmholtz, 
1863). Von Bekesy (i960) demonstrated both in models and in 
human cochleas that mechanical frequency analysis occurs, and 
that it takes the form of a distribution of the various spec- 
tral components of an auditory signal along the basilar mem- 
brane in an orderly sequence according to frequency. A limited 
resolution Fourier analysis, in conjunction with neural funnel- 
ing (von Bekesy, 1960), can account for the pitch of a pure 
tone and the absence of pitch characteristic of broad band 
noise. Tonndorf (1962) has shown that the cochlea performs 
a combined time and frequency analysis of auditory signals. 
He demonstrated time and frequency analysis in Bekesy-type 
cochlear models showing that the models' response to a sinu- 
soid closely approximated a frequency analysis and its response 
to an impulse closely approximated a time analysis. Complex 
signals distributed themselves along a continuum between 
these two extremes. 



2 . 



Complex signals consisting of sinusoids spaced at 
inharmonic intervals produce pitch matches to the middle 
portion of the energy mass (Ekdahl and Boring, 1934). Thus, 
if a number of sinusoids is placed within a restricted fre- 
quency band, listeners produce pitch matches in the center 
of the band. However, when there are only a few components 
and the components are widely spaced in frequency, the ear 
can resolve the complex into its individual components. This 
phenomenon, the analysis of a complex signal into its individ- 
ual frequency components, is called Ohm's acoustic law. Some 
investigators believe that the capacity to perform such an 
analysis depends upon the ability to discriminate the separate 
areas of mechanical excitation along the basilar membrane 
(Stevens and Davis, 1938; Greenwood, 1961). Plomp (1964) 
found that pitch matches were made individually to the lower 
five to seven spectral components of both harmonic and in- 
harmonic complex signals when the spacing of the components 
exceeded critical bandwidth at the frequency location of the 
si gnal . 

In addition to mechanical separation of components, a 
time analysis not necessarily peripheral in nature allows for 
the perception of periodicity pitch (Small, 1955), time sep- 
aration pitch (Small and McClellan, 1963; McClellan and Small, 
1965, 1966, 1967) and pitch of the residue (Schouten, Ritsma 



and Cardozo, 1962; Ritsma, 1962, 1963a, 1963b, 1967). Small 
(1955) found that amplitude-modulated (AM) signals elicited 
pitch matches corresponding to the repetition rate of the 
modulating frequency or the carrier frequency or both as 
stimulus rise-fall time, duty cycle and carrier frequency 
were varied. He suggested that perception of a periodicity 
pitch depends on the stimulus bandwidth, location of the 
spectral components, and envelope wave form fluctuation and 
not on the individual spectral components alone. 

A quasi frequency-modulated (FM) signal, consisting 
of only a carrier frequency and two sideband frequencies, has 
been used in the study of the pitch of the residue (Ritsma and 
Engel, 1964; Schouten, Ritsma and Cardozo, 1962) and certain 
phase effects (Mathes and Miller, 1947; Goldstein, 1967). 
The pitch of the quasi FM signal was matched to the pitch of 
an AM signal with the same carrier frequency when the ratio 
(f/g) of the carrier frequency (f) to the modulating frequency 
(g) was 10 or greater for the FM signal. For low values of 
f/g (i.e., less than nine) pitch matches were made to the 
modulating frequency. FM signals have also exhibited pitches 
corresponding to the carrier frequency, as well (Ritsma and 
Engel, 1964), These investigators were forced to use a 
quasi FM signal because three-component spectra occur for 
sinusoidally frequency-modulated signals only when the 



modulation index (ratio of frequency deviation to modulation 
frequency) is less than one. When the modulating index ex- 
ceeds unity, the number of sidebands increases rapidly and 
the spectrum no longer resembles that of an AM signal. 

FM auditory signals have been used in psychoacousti c 
investigations to obtain frequency difference limens (Shower 
and Biddulph, 1931; Filling, 1958; Brandt, 1967) and in ex- 
periments concerning phase perception (Goldstein, 1967; 
Mathes and Miller, 1947; Zwicker, 1962), to determine one 
pitch related to the fine structure of the wave form of an 
auditory signal (Ritsma and Engel , 1964; Fischler, 1967) and 
to specify the sensitivity to unidirectional FM (Sergeant and 
Harris , 1962) . 

The limited use that has been made of FM auditory 
signals has shown that they elicit a variety of pitch per- 
ceptions dependent upon the acoustic characteristics of the 
particular signal employed. Frequency-modulated sinusoids 
have been shown to elicit pitches related to the carrier 
frequency and to the modulation frequency. Most experiments 
involving FM signals have generally required the subject to 
match the pitch or some other psychophysical attribute of 
the FM signal to the corresponding attribute of an AM signal. 
The investigators (Ritsma and Engel, 1964; Schouten, Ritsma 
and Cardozo, 1962; Mathes and Miller, 1947; Goldstein, 1967) 



have taken special care to insure that the spectral char- 
acteristics of the FM and AM signals were as similar as 
possible. Such spectral matching of FM signals to their 
AM counterparts produces signals whose characteristics may 
not be representative of the general properties of FM signals. 

Consideration of the frequency analyzing capability 
of the ear, demonstrated by Plomp (1964) and Plomp and Mimpen 
(1968) using complex signals with various frequency spacings 
of the spectral components, suggests that the ear performs 
a limited resolution Fourier analysis on such signals and 
that an FM signal should elicit pitches corresponding to its 
individual spectral components when' the frequency spacing of 
the spectral components exceeds the critical bandwidth of the 
ear's analyzing filter at that frequency. 

The pitch of FM signals has not been systematically 
investigated in the general case. The present investigation 
is an attempt to determine the pitch or pitches elicited by 
FM signals as a function of the carrier frequency, modulating 
frequency and sensation level of the signal in a free response 
experiment , 



CHAPTER II 
PROCEDURE 

Apparatus. Frequency-modulated stimuli were generated 
by the reactance-tube modulator of a beat-frequency oscillator 
(Bruel and Kjaer, Type 1014). The modulating signal was gen- 
erated by an external oscillator (General Radio, Type 1304-B). 
The modulating signal amplitude was controlled by the oscil- 
lator attenuator and an external attenuator (Hewlett-Packard, 
350D) and was such that the extent of modulation was always 
±100 Hz. The carrier frequency was selected on the main fre- 
quency dial of the Briiel and Kjaer oscillator. The FM signal 
was split and attenuated by two pairs of attenuators in series 
(Hewlett-Packard, 350D) and fed through impedance-matching 
transformers (United Transformer Company, LS-33) to two ear- 
phones (Telephonies, TDH 39-102) to permit simultaneous lis- 
tening by two subjects. Each active earphone was mounted 
together with a dummy earphone in a standard headband. All 
earphones were fitted with MX-41/AR cushions. 

The subjects sat in an I AC sound- treat ed room (Model 
403-A). Two matching oscillators (General Radio, Type 1313A), 
two attenuators (Hewlett-Packard, 350D) and two two-position 



switches were arranged so that each subject could select 
either the experimental FM stimulus or his own unmodulated 
matching signal. The matching oscillator dials were covered 
by white cardboard discs so that no dial markings were vis- 
ible to the subjects. The frequency and intensity of the 
matching tone were under subject control. The frequency of 
each matching oscillator was read out on a frequency counter 
(Hewlett-Packard, 522B) upon indication from each subject 
that a match had been made. Figure 1 shows the arrangement 
of the equipment. 

Acoustic stimuli were analyzed using an artificial 
ear (Bruel and Kjaer, Type 4152) in' conjunction with a one- 
inch condenser microphone and cathode follower (Briiel and 
Kjaer, Type 4132/2163) and microphone amplifier (Bruel and 
Kjaer audio frequency spectrometer. Type 2112) whose output 
was fed to a wave analyzer (General Radio, 1900A) and graphic 
level recorder (General Radio, 1521B). Electrical stimuli 
were also analyzed using the wave analyzer and graphic level 
recorder and carefully monitored throughout the experiment. 
Although second harmonic distortion was present in the acoustic 
signal, the amplitude of the distortion products was 45dB or 
more below the level of the unmodulated carrier for all of 
the stimulus conditions. Earphone responses and represen- 
tative electrical spectra are to be found in Appendix A. 



FREQUENCY 
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Stimuli . Stimuli consisted of 300-, 1000- and 3000- 
Hz sinusoids, each f r equen cy -modul at ed by sinusoids of 20, 
200 and 2000 Hz (the latter only for the 3000-Hz carrier 
frequency). The frequency deviation in Hz from the carrier 
frequency was always i:100 Hz. Stimulus intensities of 20 and 
50dB relative to the subject's threshold were used. All con- 
ditions were randomized except that when two subjects lis- 
tened simultaneously, they were both presented the same FM 
signal. The experimental conditions are listed in Table 1, 



■ Table 1. Experimental Conditions. The X's in the table represent 
combinations of modulating and carrier frequencies. 



20dB Sensation Level 50dB Sensation Level 
Modulating Carrier Frequency Carrier Frequency 
Frequency 300 1000 3000 300 1000 3000 




Subjects . Five normal-hearing adults, who demonstrated 
the ability to pitch match to the unmodulated carrier frequency 
with no more than one semitone frequency error, were used as 
subjects. Normal hearing was defined for purposes of this 
experiment as no loss greater than 15dB (re. ISO, 1964 standards) 



10 



at any octave frequency over the range from 125 to 8000 Hz. 
General procedure . Subjects were seated comfortably 
in the sound booth with the stimulus switch, matching oscil- 
lator and attenuator arranged for the individual subjects' 
convenience. Instructions were presented to the subject on 
a typed card and the investigator answered any questions 
after the subject had read the card. The instructions were: 

1. Listen to the signal to become familiar with it. 

2. Match to the most obvious pitch or pitches. 

3. Search for other pitches in the signal. There 
may be one or as many as seven or more. They 
may sound close together or far apart. 

4. Match to all the pitches. 

5. Once the pitches are established, speed should 
be increased while maintaining accuracy. 

6. If you should become tired, either turn the 
switch to the "off" position for awhile, or 
leave the booth for a break. 

Subjects were permitted to listen to the stimulus as 
long as they wished, and to switch back and forth between 
stimulus and matching signal as they wished before they in- 
dicated a match. They were allowed to vary the intensity of. 
the matching stimulus if so desired. Most listeners preferred 
the two stimuli to be approximately equal in loudness. A five- 
minute break was mandatory after each 30-minute pitch matching 
period if the subject did not choose to rest at more frequent 
interval s . 



CHAPTER III 
RESULTS 

Data were collected in the form of pitch matches to 
sinusoidally frequency-modulated sinusoids with carrier 
frequencies of 300, 1000 and 3000 Hz, Modulating frequen- 
cies of '20, 200 and 2000 Hz were used, the latter for the 
3000-Hz carrier frequency only. The frequency deviation 
about the carrier frequency was held constant at +100 Hz 
for. all stimuli. Stimuli were presented at 20dB and 50dB 
above the subject's threshold for the FM signal. The lis- 
teners were instructed to match an unmodulated sinusoid to 
any and all pitches they perceived in the FM stimulus. 

Two-hundred pitch matches were obtained from each of 
the five listeners resulting in a total of 1000 pitch matches 
for each of the 14 stimulus conditions. The pitch matches 
were tallied as deviations from the carrier frequency in 
20-cent intervals. Individual listener data are shown graph- 
ically in Appendix B, 

Figures 2, 3, 4, 5, 6 and 7 are composite figures 
showing the combined data from all listeners for each con- 
dition in terms of the deviation of pitch matches from the 

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17 




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rOrOojcM— — — — — 

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carrier frequency in 20-cent intervals. A second scale is 
included on each of the figures to show the frequency (in 
Hz) of the matches. The arrows found above the histograms 
in the figures represent the locations of spectral components 
in the electrical signal when the modulation frequency is 
200 or 2000 Hz. The arrows found above the histograms of 
data gathered with a 20-Hz modulation frequency only represent 
the 3dB-down points on the sharp slopes of the very narrow 
band spectra. 

.Effects of modulation frequency ( 20dB SL) . Generally, 
pitch matches to 20dB SL stimuli modulated at a 20-Hz rate 
lie within the frequency band containing the spectral energy 
of the stimulus. At the 300-Hz carrier frequency modulated 
at a 20-Hz rate (300/20) the majority of the matches (Fig. 2A) 
are distributed between the carrier frequency and the upper 
extreme of the band of spectral energy with relatively few 
matches occurring to frequencies below the carrier frequency. 
The distribution of matches to the 1000/20 (Fi'g. 3A) stimuli 
has a prominent maximum near the lower frequency extent of 
the energy, band and a second less prominent maximum near the 
upper frequency extent of the energy band. The distribution 
of matches to the 3000/20 (Fig. 4A) stimulus condition is 
approximately unimodal although skewed from the lower extent 
of the energy band. An abrupt decrease in number of matches 



19 

at the upper and lower extents of the energy band is also 
evident . 

The distributions of pitch matches to the 300/200 
(Fig. 2B) and 1000/200 (Fig. 3B) conditions are multi-modal 
with definite maxima occurring at the frequencies of the 
spectral components present in the stimulus. The single 
exception occurs in the 300/200 condition (Fig. 2B) where, 
in addition to pitch matches to the spectral components, 
pitch matches corresponding to the modulation frequency are 
found although no spectral component exists at that frequency. 
This exception will be discussed in detail later. The dis- 
tribution of matches to the 3000/200 (Fig. 4B) conditions 
had a large maximum centered about the carrier frequency and 
some indication of secondary maxima near the upper and lower 
extents of the energy distribution. The 3000/2000 stimulus 
conditions elicited pitch matches whose distribution exhibited 
a large maximum at the carrier frequency (Fig. 3C). 

The general character of the distribution of pitch 
matches to stimuli modulated at a 20-Hz rate did not change 
as the carrier frequency was increased. The pitch matches 
generally fell at or within the limits of the spectral band- 
width. As the carrier frequency was increased, the distribu- 
tion of pitch matches to stimuli modulated at a 200-Hz rate 
changed from multimodal with definite maxima at the frequencies 



20 



of the spectral components of the stimulus to unimodal with 
a maximum at the carrier frequency in the case of the 3000/200 
stimulus. The 2000-Hz modulating frequency was used only in 
conjunction with the 3000-Hz carrier frequency because it is 
not possible to modulate a signal with one of higher frequency 
The distribution of pitch matches elicited by the 3000/2000 
stimulus condition exhibited very definite maxima at the car- 
rier frequency and at 1000 Hz, the frequency of the first 
spectral component on the low frequency side of the carrier 
frequency. Pitch matches did not occur to the first upper 
spectral component of the 3000/2000 stimulus. 

Effects of modulation frequency ( 50dB SL ) . An increase 
in the intensity of the stimulus from 20dB SL to 50dB SL pro- 
duced no change in the major configuration of the distribu- 
tion of responses to the 300/20, 1000/20, 3000/20 and 3000/200 
stimulus conditions although the increase in intensity did 
tend to restrict the frequency extent of the matches. The 
pitch matches remained at or within the extent of the spectral 
bandwidth. The increase in stimulus intensity from 20dB to 
50dB SL for the 300/200, 1000/200 and 3000/2000 conditions 
resulted in pitch matches to additional audible spectral com- 
ponents to which pitch matches did not occur at the low stim- 
ulus intensity. The additional pitch matches occurred to a 
spectral component on the high side of the energy band in the 



21 



cases of the 300/200 and 1000/200 conditions and to the 
spectral component on the low side of the energy band in 
the case of the 3000/2000 condition. 

Sub.iect variability . Examination of the pitch match 
data of individual subjects reveals a marked difference be- 
tween the kinds of pitch match distributions obtained from 
subjects JH and CH and those obtained from subjects DF , NM 
and TM. The pitch match distributions produced by JH and CH 
were consistently unimodal and centered on or near the carrier 
frequency while the distributions of pitch matches for DF , NM 
and TM were generally more representative of the spectral 
energy distributions of the respective stimuli. 

Between-subject variability is illustrated in Figure 8. 
The distribution of pitch matches elicited by the 1000/200 
stimulus presented at 50dB SL from each of the five subjects 
is shown on a common frequency deviation scale with the fre- 
quency location of the spectral components of the stimulus 
shown by inverted arrowheads. Subjects DF , NM and TM ex- 
hibited definite groups of pitch matches to 3, 7 and 2 spec- 
tral components respectively, while subjects CH and JH did 
not exhibit well defined groups of pitch matches that could 
be related to the stimulus spectrum. 

The most common pitch judgments w*hich occur consis- 
tently enough to produce discernible maxima in the distri- 
bution of pitch matches to other than spectral information 



22 




u 

••+J 
(d 
B 

j2 

o 

o 

Q 

■'-3 

^ 

3 

«3 

I 

fl 

Cl> 

+-> 

0) 

o 

c 



■H 
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03 



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Cs2 


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S3H01VIM Hoiid Ao aaaiAinN 



23 



were judgments representing octave relationships to spectral 
components. Octave judgments, or more commonly, octave 
"errors," occurred at 150, 200 and 400 Hz in the 300/200, 
20dB condition (Fig. 2B) and at 2000 and 4000 Hz in the 3000/ 
2000, 50dB condition (Fig, 7C ) , Constant errors, of course, 
were also found to exist. 



CHAPTER IV 
DISCUSSION 

Frequency-modulated sinusoids have been shown to 
elicit a variety of auditory sensations whose character 
varies as a function of modulation rate. Very slow mod- 
ulation rates have been used to study differential thresh- 
olds for frequency (Shower and Biddulph, 1931; Filling, 
1958; Brandt, 1967). Utilizing a low modulation frequency 
(2-3 Hz), the just noticeable change in pitch of an FM 1000- 
Hz sinusoid occurs when the extent of modulation ranges from 
^5-10 Hz. In these experiments the pitch change is asso- 
ciated only with modulation of the carrier frequency. From 
modulation frequencies of one Hz to approximately 10 Hz, a 
listener hears a single tone rising and falling in pitch at 
the modulation rate. A modulation frequency of 20 Hz elicits 
perception of a complex warbling or fluttering sound. The 
warbling changes to a roughness and disappears as the mod- 
ulating frequency is increased, leaving the perception of a 
complex auditory signal. The pitch (es) of FM sinusoids with 
modulation frequencies greater than 20 Hz become dependent 
upon the parameters of the signal. 

24 



25 



The spectral distribution of the energy of an FM sig- 
nal is a function of the modulating frequency in conjunction 
with the modulation index. The frequency spacing of the spec- 
tral components (sidebands) is determined by the modulating 
frequency and is equal to it. The amplitude of the various 
spectral components is dependent upon a complex function known 
as a Bessel function. The bandwidth of an FM signal is defined 
as the width of the frequency spectrum that contains all com- 
ponents having an amplitude of 1 percent or greater relative 
to the amplitude of the unmodulated wave (Sheingold, 1951). 
The number of significant spectral components in an FM signal 
increases when the modulation index is increased. 

Pitch matches to the modulating frequency of a quasi- 
FM signal have been obtained (Ritsma and Engel , 1964). The 
stimulus used to elicit these pitch matches had a ratio, n, 
of carrier frequency to modulating frequency of five or six 
and a modulation index of 2.55. The investigators stated that 
the modulation index should be as large as possible and that 
n should be small (less than five or six) to produce pitch 
matches to the modulating frequency. In addition, it might 
also be stated that the carrier frequency must be 2000 Hz or 
higher. Carrier frequencies, modulating frequencies, n ' s 
and modulation indexes of the stimuli used in the present 
investigation appear in Table 2. An asterisk beside an entry 



Table 2. Frequency modulation stimulus parameters. 



26 



Cf (Hz) Mf (Hz) 



n: 



Cf 

'Mf 



Mod . Index = ^^ 



Mf 



300 


20 


15 


300 


. 200 


1 . 5* 


1000 


20 


50 


1000 


200 


5* 


3000 


20 


150 


3000 


200 


15 


3000 


2000 


1 . 5* 



5* 



5* 



5* 



5 
05 



Af measured one way from the carrier frequency was 
always 100 Hz in all stimulus conditions. 



27 

in the table indicates that the associated tabled value 
meets the criterion of Ritsma and Engel for the production 
of pitch matches to the modulation frequency. Inspection of 
the table shows that none of the stimuli used in the present 
investigation meet both of the Ritsma and Engel criteria 
necessary to elicit pitch matches to the modulation frequency. 
However, in the present experiment, one experimental condi- 
tion produced pitch matches which seemed related to the mod- 
ulation frequency. 

The 300/200, 20dB SL stimulus condition produced a 
substantial number of pitch matches centered on 200 Hz where 
no spectral energy was present in the stimulus (Fig. 2A) . 
Although periodicity is a possible explanation for the matches 
that occurred at 200 Hz, it is difficult to reconcile such an 
explanation with the fact that the experimental conditions 
do not meet the conditions cited above as requisite for such 
pitch judgments. An alternative explanation follows. 

While not as prominent as the pitch matches at 200 Hz, 
substantial groups of matches also occurred at 100 and 400 Hz. 
Since 200 and 400 Hz are the second and fourth octaves of 100 
Hz, there is the possibility that the groups of matches to 
200 and 400 Hz may represent octave errors of the 100-Hz 
spectral component which is present. In addition, the clus- 
ters of pitch matches which occur at 200 and 400 Hz in response 



28 



to the 300/200-Hz condition at 20dB SL are generally absent 
in the distribution of matches obtained at 50dB SL. Although 
the 100-Hz spectral component is audible at the 20dB SL pre- 
sentation level (Appendix A, Fig. IIB), its increased inten- 
sity at the 50dB SL presentation level may permit more accu- 
rate pitch judgments and reduce the number of octave errors. 
It should also be noted that almost all of the pitch judgments 
at 200 and 400 Hz at 20dB SL are the result of subjects DF and 
TM (Appendix B, Figs. 17 and 25 respectively). 

Pitch matches to the 200/20 condition lie within the 
frequency band of the spectral energy of the stimulus, but 
the majority of the matches occurred at frequencies between 
the middle and the upper end of the spectral energy distribu- 
tion. This result can be explained on the basis of the abso- 
lute sensitivity of the ear as a function of frequency (Fig. 
9) where the sensitivity of the ear decreases rapidly below 
300 Hz and continues to increase from 300 Hz up to about two 
kHz. Since the spectral energy distribution of the 300/20 
condition is relatively symmetrical about the carrier fre- 
quency, the sensation level of the stimulus will be slightly 
higher on the high frequency side of the energy band, where 
the matches predominantly occur. 

The 300/20, 1000/20 and 3000/20 stimulus conditions 
have spectral energy distributions whose individual components 



29 




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o 



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1 


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1 



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c 



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c 

3 



to 

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a; 
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CO 

■*-> 02 



(g^MO/BNAQ i=ap oyaz) a? m annssaad 



w 


> 


c 


a 


0) 


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30 



are spaced at 20-Hz intervals. The frequency extents of the 
energy bands of these stimuli are marked by quite abrupt 
decreases in spectral energy (Appendix A, Figs. llA, l 2A 
and 13A) . Pitch match data obtained by von Bekesy (1963) 
in response to band-pass filtered noise, and by Small and 
Daniloff (1967) in response to low- and high-pass filtered 
noise show the pitch of these signals to be related to the 
end or ends of the noise band where the steep gradient in 
energy vs. frequency occurs. Data from the present experi- 
ment also exhibit pitch matches in response to the ends of 
the energy, band and suggest the possibility that such pitch 
matches might be the result of a slope detector or peripheral 
"edge effect" and neural funneling in the sense of von Bekesy 
(1960) . 

An alternative explanation which seems to incorporate 
all the data may be found in the concept of the critial band 
hypothesis. Consideration of the critical band data of Plomp 
and Mimpen (1968) (Fig. 10) shows the critical band, or min- 
imum frequency separation necessary for spectral components 
of a complex signal to be heard individually, to be approxi- 
mately 60 Hz. The spectral component separation of the 300/ 
20, 1000/20 and 3000/20 conditions is only 20 Hz. A critical 
band hypothesis would predict that the individual spectral 
components of such signals could not be heard individually 



31 



y 3 
UJ 

o 



UJ 

u. 

Ll. 
Q 

> 
o 

Z 
LU 

=) 
O 
UJ 

cr 



10 



— ■ • ..II 11 I I I I II I I I I _ 



10' 



5 10* 
FREQUENCY (HZ) 



10' 



Figure 10. Critical bandwidth based on the minimum frequency 
difference between the harmonics of a complex tone necessary 
for them to be heard separately, as a function of frequency 
(after Plomp and -Mimpen, 1968). 



32 



and that pitch matches in response to such stimuli should, 
therefore, not distribute themselves according to the indi- 
vidual spectral component frequency locations of the signals. 
Indeed, pitch matches in response to stimuli with a 20-Hz 
modulation frequency used in the present investigation do 
not distribute themselves according to the individual spec- 
tral components present in the stimuli as expected from the 
critical band hypothesis. Responses to the 1000/20 stimulus 
condition distribute themselves bimodally with a mode occur- 
ring at each end of the frequency band occupied by the spec- 
tral energy. The mode at the high frequency end of the energy 
band was more pronounced for responses to the 50dB SL presen- 
tation level (Fig, 6A) than for responses to the 20dB SL pre- 
sentation level (Fig. 3A) . The critical bandwidth at 1000 Hz 
is approximately 175 Hz. The bandwidth of the stimulus energy 
was approximately 500 Hz. The bimodal nature of the response 
distribution to the 1000/20 stimulus condition could result 
from activity in the adjacent critical bands above and below 
the one containing the carrier frequency of the FM signal. 
The distribution of pitch matches to the 3000/20 stimulus con- 
dition was broad and unimodal with an abrupt decrease in num- 
ber of matches above and below the frequency extents of the 
stimulus bandwidth (Figs. 4 and 7). Critical bandwidth at 
3000 Hz is approximately 500 Hz, which coincides with the 



33 



bandwidth of the 3000/20 stimulus and confines the entire 
stimulus complex to one critical band. 

The critical bandwidth is less than 200 Hz at 300 
and 1000 Hz. With one exception, previously discussed, 
pitch matches to the 300/200 and 1000/200 stimuli formed 
distributions representative of the audible spectral com- 
ponents present in the stimuli. An additional spectral com- 
ponent became audible at 900 Hz when the 300/200 stimulus 
was increased from 20dB SL to 50dB SL , and at 1600 Hz when 
the 1000/200 stimulus was increased from 20dB to 50dB SL 
(Figs. 2, 3, 5 and 6). Pitch matches occurred at the fre- 
quencies of these components when the higher ( 50dB SL) stim- 
uli were presented, but not when the 20dB SL stimuli were 
presented. These responses suggest a long term frequency 
analysis as a basis for the pitch perceptions elicited. At 
the 3000-Hz carrier frequency, 200 Hz is less than critical 
bandwidth while 2000 Hz exceeds critical bandwidth. Pitch 
match distributions in response to the 3000/200 stimulus at 
both the 20dB SL and 50dB SL presentation levels are similar 
in character and frequency extent to the distribution of 
matches obtained in response to the 3000/20 stimuli. The 
3000/2000 stimuli, however, elicited response distributions 
similar to those obtained in response to the 300/200 and 1000/ 
200 stimulus conditions. At 20dB SL presentation level, only 



34 



the spectral component located at the carrier frequency was 
of sufficient intensity to be audible. The response dis- 
tribution consisted of a single shar ply- f r equency-delimi ted 
cluster of pitch matches located at the 3000-Hz carrier fre- 
quency. When the presentation level was increased to 50dB 
SL , the 1000-Hz spectral component was sufficiently intense 
to be audible, and a second well-defined group of pitch 
matches occurred at 1000 Hz. The lack of pitch matches to 
the 5000-Hz spectral component can be accounted for by the 
rapid decrease in the sensitivity of the ear between 3000 Hz 
and 5000 Hz (Fig. 9) . 

Spectral components of the stimuli used in the in- 
vestigation by Plomp and Mimpen (1968), from which the crit- 
ical band data of Figure 10 are taken, did not vary in fre- 
quency as a function of time. The individual spectral com- 
ponents that made up the various test stimuli used in the 
present investigation varied in instantaneous frequency as 
a function of the modulating frequency and the frequency swing 
of the carrier. Frequency deviation was held constant at 
:tlOO Hz so that all of the spectral components of the stim- 
uli were varying sinusoidally over a 200-Hz frequency extent 
at the rate of the modulating frequency. When the spectral 
component frequency spacing of the FM signals used in the 
present investi'gation exceeded critical bandwidth (Fig. 10) 



pitch matches wex^e made to the averaged frequency location 
of the respective frequency components. Such pitch matches 
suggest that the ear is able to perform a long-term spectral, 
or Fourier, analysis upon complex ongoing auditory signals 
provided that the spacing of the components of the complex 
exceeds the resolving power of the ear's analyzing system 
for the frequencies involved. A system of filters is the 
hypothetical mechanism of choice. The critical band is a 
measure of the limits of the resolving power of the ear's 
filter system. Pitch match distributions in response to 
each of the experimental stimuli whose spectral component 
frequency spacing exceeded critical' bandwidth were based 
upon the frequency locations of the spectral components. 
Pitch match distributions in response to each of the experi- 
mental stimuli whose spectral component frequency spacing was 
smaller than critical bandwidth were based upon the extents 
of the energy band, the center of the energy band or some 
other aspect of the energy distribution not related to the 
individual spectral components. 

The amplitude of the various spectral components rel- 
ative to the sensitivity of the ear at the frequency loca- 
tions of those components determines the particular compo- 
nents that will be heard provided that critical bandwidth 
spacing is exceeded. In every case, when stimuli whose 



36 



spectral component spacing exceeded critical bandwidth were 
increased in amplitude by 30dB SL , an additional spectral 
component became audible and pitch matches occurred in re- 
s ponse to it. 



CHAPTER V 

SUMMARY 

Frequency-modulated (FM) and quasi FM signals have 
been used as stimuli in psychoacous ti c experiments in the 
study of frequency difference limens, pitch of the residue 
and phase perception and have been demonstrated to elicit 
a variety of pitch perceptions dependent upon acoustic char- 
acteristics of the signal used. FM sinusoids have been shown 
to elicit pitches related to the carrier frequency and modu- 
lating frequency. This investigation determined the pitch or 
pitches elicited by FM sinusoids as a function of the carrier 
frequency and the modulating frequency at two sensation levels 
of the si gnal . 

Fourteen stimulus conditions were used. Stimuli con- 
sisted of 300-, 1000- and 3000-Hz sinusoids, frequency modu- 
lated at modulation frequencies of 20, 200 and 2000 Hz (only 
for the 3000-Hz carrier frequency). The frequency deviation 
in Hz from the carrier frequency was always +100 Hz. Stimulus 
intensities of 20 and 50dB relative to the subject's thresh- 
old were used. Five normal hearing adults who demonstrated 
the ability to pitch match to the unmodulated carrier frequency 

37 



38 



with no moi-e than one semi-tone frequency error were used 
as subjects. Stimuli were presented monaurally. Subjects 
were permitted to listen to the stimuli as long as they 
wished, and to switch back and forth between the FM stim- 
ulus and matching signal (an unmodulated sinusoid) as often 
as they wished before they indicated a match. 

In general, the nature of the pitch match distribu- 
tions obtained in response to FM sinusoids was dependent 
upon the frequency spacing of the individual spectral com- 
ponents of the stimulus. Pitch matches occurred to individ- 
ual spectral components when spectral component frequency 
spacing exceeded critical bandwidth. When spectral component 
frequency spacing was less than critical bandwidth, pitch 
matches occurred to the center and/or the ends of the band 
of spectral energy. 

While an increase in the intensity of stimuli with 
less than critical bandwidth spectral component spacing changed 
the pitch match distribution to that condition very little, the 
same increase in the intensity of stimuli with greater than 
critical bandwidth spectral component spacing caused an addi- 
tional component to become audible and pitch matches occurred 
to the additional component. In only one stimulus condition 
did the listeners not match to spectral energy. Such matches 



39 



corresponded to the modulating frequency. With all of the 
data considered, these matches were explained as octave 
judgments to a spectral component. Thus, no pitch matches 
occurred to modulation frequencies but rather to spectral 
energy present in the acoustic signal. 

All of the individual spectral components that made 
up the various test stimuli used in the present investigation 
varied in instantaneous frequency as a function of the modu- 
lating frequency and the frequency swing of the carrier. 
V/hen the spectral component frequency spacing of the FM 
signals exceeded critical bandwidth, pitch matches were made 
to the averaged frequency location of the respective frequency 
components. Such pitch matches suggest that the ear is able 
to perform a long-term spectral, or Fourier, analysis upon 
complex ongoing auditory signals provided that the spacing 
of the components of the complex exceeds the resolving power 
of the ear's analyzing system for the frequencies involved. 
A system of filters which increase in bandwidth with fre- 
quency in the same fashion as traditional critical band ana- 
lyzers is the hypothetical mechanism of choice. 



APPENDICES 



APPENDIX A 

ELECTRICAL SPECTRA AND 
EARPHONE FREQUENCY RESPONSE CURVES 



Electrical spectra of the experimental stimuli were 
obtained using a wave analyzer (General Radio, 1900A) and 
a graphic level recorder (General Radio, 1521B). The wave 
analyzer bandwidth was 10 Hz. The recorder chart speed was 
five inches per minute and the recorder writing speed was 
10 inches per second. Zero dB was equivalent to the ampli- 
tude of the unmodulated carrier signal (Figures 11, 12, 13, 
14) . 

Earphone frequency response curves for the two tele- 
phonics TDH-39 lOZ earphones were obtained using a beat fre- 
quency oscillator (General Radio, 1304B) as a signal source. 
An artificial ear (Bruel and Kjaer, 4152), condenser micro- 
phone (Bruel and Kjaer, 4132), cathode follower (Briiel and 
Kjaer, 2163) and microphone amplifier (Briiel and Kjaer audio 
frequency spectrometer, 2112) supplied the input to a graphic 
level recorder (General Radio, 1521B) from the acoustic out- 
put of the earphone (Figures 15, 16), 



41 



42 



CD 

T3 

u 

Q 

n 

_l 
Q. 



-lU 








-20 


- 






-50 


- 


A 


300/20 


-40 


- 






-50 


- 






-60 


- 






-70 


- 






-80 










! 1 1 1 1 1 1 


1 1 1 1 1 1 







500 1000 

FREQUENCY (HZ) 



1500 



2000 



CQ 

LU 
Q 

_J 

< 



-lU 
















-20 


- 










-30 


- 








B 


300/200 


-40 


- 












-50 


- 














-60 








- 








-70 


— 














-80 


















1 


1 


1 


1 


1 ! 1 1 1 


1 1 1 1 1 1 



500 1000 

FREQUENCY (HZ) 



1500 



2000 



Figure 11. Electrical spectra for 300/20 CA) and 300/200 (B) 

Analyzing bandwidth was 10 Hz. 



43 



CD 

LU 
Q 

3 



a. 
< 



-10 

-20 
-30 
-40 
-50 
-60 

-70 
-80 



A 1000/20 



500 1000 

FREQUENCY (HZ) 



1500 



2000 



. -lu 
-20 


- 




















-30 


- 






1 B 1000/200 


m 

■a 














Z -40 
o 

13 -50 
a. 

< 


















-60 




















-70 






















-80 






















\J\J 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 1 



500 1000 

FREQUENCY (HZ) 



1500 



2000 



Figure 12. Electrical spectra for 1000/20 (A) and 1000/200 
CB). Analyzing bandwidth was 10 Hz. 



m 



-iO r 



2000 



A 3000/20 




2500 



T 
3000 
FREQUENCY (HZ) 



Figure 13. Electrical spectra for 3000/20 (A) and 3000/200 
(B). Analyzing bandwidth was 10 Hz. 



45 



O 
O 

o 

CM 
O 

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APPENDIX B 
INDIVIDUAL SUBJECT PITCH MATCH DATA 

Pitch matches are plotted as deviations in semi-tones 
of pitch judgments in 20-cent intervals from the carrier fre- 
quency for subjects DF (Figures 17, 18, 19, 20), NM (Figures 
21, 22, 23, 24), TM (Figures 25, 26, 27, 28), CH (Figures 29, 
30, 31, 32), and JH (Figures 33, 34, 35, 36). The arrows 
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BIBLIOGRAPHY 



von Bekesy, G., ( 1960 ). Ex periment s in Hearing (McGraw- 
Hill Book Company, New York), 

von Bekesy, G., (1963), "Hearing Theories and Complex 
Sounds," J . Acoust . Soc . Am . 35, 588-601. 

Brandt, J. F,, (1967). "Frequency Discrimination Following 
Exposure to Noise," J . Acoust . Soc . Am . . 41, 448-457. 

Ekdahl, A. G., and Boring, E. G., (1934). "The Pitch of 
Tonal Masses," Am. J . Psychol . . 46, 452-455. 

Filling, S., (1958). Difference Limen for Frequency 
( Andelsbogtrykkeriet-Copenhagen , I Obense). 

Fischler, H., (1967). "Model of the 'Secondary' Residue 

Effect in the Perception of Complex Tones," J. Acoust . 
Soc . Am . . 42, 759-764, 

Goldstein, J, L., (1967). "Audi tory' S pec tral Filtering and 
Monaural Phase Perception," J . Acoust . Soc . Am . . 41, 
458-479. 

Greenwood, D. D., (1961). "Auditory Masking and the Critical 
Band," J . Acou'St . Soc . Am . , 33, 413-417. 

von Helmholtz, H, L, F., (1863). Die Lehre von den Tonemofin - 
dugen als phv si ologi sche Grundlage fur die Theorie der 
Musik (F. Vieweg and Sohn , Brauschweig) , in (1954). On 
the Sensations of Tone ^ 2nd English translation by A. L. 
Ellis (Dover Publications, Inc., New York). 

McClellan, M, E., and Small, A. M., Jr , (1967). "Pitch 

Perception of Pulse Pairs with Random Repetition Rate," 
J . Acoust . Soc . Am . ■ 41, 690-699. 

McClellan, M. E., and Small, A. M., Jr., (1965). "Time 
Separation Pitch Associated with Correlated Noise 
Bursts," J . Acoust , Soc . Am . . 38, 142-143. 



69 



70 



-McClellan, M. E., and Small, A. M., Jr., (1966). "Time 
Separation Pitch Associated with Noise Pulses," _J. 
Acoust ■ Soc ■ Am . . 40, 570-582. 

Mathes, R. C, and Miller, R. L., (1947). "Phase Effects 
in Monaural Phase Perception," J. Acoust. Spc. Am .. 
19 , 780-797 . 

Plomp, R., (1964). "The Ear as a Frequency Analyzer," 
J . Acoust . Soc ■ Am . . 36, 1628-1636. 

Plomp, R., and Mimpen , A. M., (1968). "The Ear as a Fre- 
quency Analyzer, II.," J . Acoust . Soc . Am . . 43, 764- 
767 . 

Ritsma, R. J. (1962). "Existence Region of the Tonal 
Residue. I," J . Acoust . Soc . Am . , 34, 1224-1229. 

Ritsma, R. J., (1963a). "Existence Region of the Tonal 
Residue II," J . Acoust . Soc . Am . . 35, 1241-1245. 

Ritsma, R. J., (1967). "Frequencies Dominant in the Per- 
ception of the Pitch of Complex Sounds," J. Acoust . 
Soc. Am . . 42, 191-198. 

Ritsma, R. J., (1963b). "On Pitch Discrimination of 
Residue Tones," Int . Audiol . . 2, 34-37. 

Ritsma, R. J., and Engel , F. L., (1964). "Pitch of 

Frequency-Modulated Signals," J . Acoust . Soc . Am . . 
36, 1637-1644. 

Schouten, J. F., Ritsma, R. J., and Cardozo, B. L., (1962). 
"Pitch of the Residue," J . Acoust . Spc . Am . . 34, 1418- 

1424. 

Sergeant, R. L., and Harris, J. D., (1962). "Sensitivity 
to Unidirectional Frequency Modulation," J . Acoust . 
Soc ■ Am . . 34, 1625-1628. 



Sheingold, A., (1951), Fundamentals of Radio Communication 
(D, Van Nostrand Company, Inc., Princeton). 

Shower, E. G., and Biddulph, R., (1931). "Differential 

Pitch Sensitivity of the Ear," J . Acoust Soc . Am . . 3, 
276-287. 



71 



Suiall, A. M., Jr. (1955). "Some Parameters Influencing 

the Pitch of Amplitude Modulated Signals," J . Acoust . 
Soc ■ Ain ■ , 27, 751. 

Small, A. M., Jr. and D anil off, R. G., (1967). "Pitch 
of Noise Bands," J . Acoust . Spc . Am . . 41, 506-512. 

Small, A. M., Jr., and McClellan, M. E., (1963). "Pitch 

Associated with Time Delay between Two Pulse Trains," 
J ■ Acoust. Soc . Am ■ . 35, 1246-1255. 

Stevens, S. S., and Davis, H., (1938). Hearing (John Wiley 
and Sons, Inc., New York). 



Tonndorf, J., (1962). "Time/Frequency Analysis along the 

Partition of Cochlear Models: A Modified Place Concept," 
J . Acoust ■ Soc . Am . , 34, 1337-1350. 

Zwicker, E., (1962). "Direct Comparisons between the Sensa- 
tions Produced by Frequency Modulation and Amplitude 
Modulation," J . Acoust . Soc . Am . . 34, 1425-1430. 



BIOGRAPHICAL SKETCH 

Keener Delaney McClelland was born November 30, 
1936, at Bristol, Virginia. In June 1954 he was grad- 
uated from Knoxville East High SchooL He received the 
degree of Bachelor of Arts with a major in Geology from 
the University of Tennessee in March 1961. From 1961 until 
1962 he served in the United States Air Force and was sta- 
tioned in Germany. In 1963 he enrolled into Graduate School 
of the University of Tennessee, and held a traineeship from 
the Vocational Rehabilitation Administration until March 
1964 when he received the degree of Master of Arts with a 
major in Audiology. From 1964 until 1965 he served as Clin- 
ical Audiologist at The Jewish Hospital of St. Louis in St. 
Louis, Missouri. In 1965 he enrolled in the Graduate School 
of the University of Florida, and held a fellowship in the 
Department of Speech while pursuing his work toward the 
degree of Doctor of Philosophy, 

Mr. McClelland is married to the former Nancy Dianne 
Newton. He is a member of the American Speech and Hearing 
Association, The Acoustical Society of America and The 
American Association for the Advancement of Science. 



72 



This dissertation was prepared under the direction of 
the chairman of the candidate's supervisory committee and has 
been approved by all members of that committee. It was sub- 
mitted to the Dean of the College of Arts and Sciences and to 
the Graduate Council, and was approved as partial fulfillment 
of the requirements for the degree of Doctor of Philosophy. 



August 27, 196i 







/^u^-ga.. 



Dean, Collpg'e 6f Aft-ts and Sciences 



Dean, Graduate School 



SUPERVi-SORY COMMITTEE: 













?-.. 



60 15